学部・大学院区分
Undergraduate / Graduate | | 理学部 | | 時間割コード
Registration Code | | 0680180 | | 科目区分
Course Category | | 専門科目
Specialized Courses | | 科目名 【日本語】
Course Title | | [G30]統計物理学３ | | 科目名 【英語】
Course Title | | [G30]Statistical Physics III | | コースナンバリングコード
Course Numbering Code | | | | 担当教員 【日本語】
Instructor | | WOJDYLO John Andrew ○ | | 担当教員 【英語】
Instructor | | WOJDYLO John Andrew ○ | | 単位数
Credits | | 2 | | 開講期・開講時間帯
Term / Day / Period | | 春 火曜日 ５時限
Spring Tue 5 | | 授業形態
Course style | | 講義
Lecture | | 学科・専攻
Department / Program | | | | 必修・選択
Compulsory / Selected | | | Compulsory for students intending to join certain research labs; optional for the others. Check with the lab that you have been assigned to. |
| |
授業の目的 【日本語】
Goals of the Course(JPN) | | | | 授業の目的 【英語】
Goals of the Course | | Statistical Mechanics is one of the major fields of physics: around 30% of Physics Nobel Prizes have been awarded for discoveries directly or indirectly related to Statistical Mechanics, particularly quantum many-body systems, many-body systems in the classical limit, other condensed matter physics, phase transitions and field theories (including the 2024 Nobel Prize in Physics). The principles and methods are applicable in many fields of physics, including condensed matter physics (e.g. Bose Einstein Condensation, superconductivity, materials science) and high energy physics (spontaneous symmetry breaking, lattice gauge field theories, the Higgs Mechanism (which is a type of phase transition) and so on) as well as astrophysics (neutron stars, simulations of galaxy evolution, and so on). The principles and methods are also applicable in a very wide variety of fields outside physics, such as biology, neuroscience, modelling of pandemics, network theory, machine learning and artificial intelligence. G30 students in the past have shown that students in chemistry, chemical engineering and materials science with a thorough grounding in the principles of Statistical Mechanics have a significant advantage over their peers who do not possess this grounding.
At the end of this course, students will have mastered basic aspects of quantum statistics of ideal gases, statistical mechanics of systems of interacting particles, and the theory of phase transitions and critical phenomena, including modern topics such as the scaling hypothesis, an introduction to renormalization group theory (the spatial renormalization group), and the Bogolyubov Variational Theorem and its application to constructing an optimal Mean Field Theory.
In this course, students learn quantum statistics of ideal gases, introductory statistical mechanics of systems of interacting particles, introductory theory of phase transitions and critical phenomena, Mean Field Theory, and some modern theory such as the scaling hypothesis, an introduction to renormalization group theory (the spatial renormalization group), and the Bogolyubov Variational Theorem and its application to constructing an optimal Mean Field Theory. Students will encounter the ideas of spontaneous symmetry breaking, universality, critical exponents, transformation between -- proof of equivalence of -- various models such as the Two-state Ising Model, Lattice Gas Model, Binary Alloy Model and Two-state Potts Model.
At the end of Statistical Physics III students will be adequately prepared with regards to their knowledge of statistical mechanics and thermodynamics to undertake further studies in Sc-lab, St-lab, R-lab, TB-lab, E-lab, H-lab, QG-lab and other, including experimental, labs in both the Department of Physics and Department of Applied Physics (Tanaka Lab), as well as chemistry and computational biology labs at Nagoya University. Students in the high energy physics labs and theoretical condensed matter physics labs should also have studied Quantum Mechanics II and be concurrently enrolled in Quantum Mechanics III.
NOTICE TO PROSPECTIVE NUPACE (exchange) STUDENTS
Prospective exchange students should be aware that the Nagoya University Department of Physics screens incoming exchange students and rejects or accepts them irrespective of whatever assurances they have been given by their home university or Nagoya University staff in other departments. This means it is possible that you have come all this way to Japan with the intention of continuing your undergraduate degree in Physics but will not be permitted to do so.
If you are interested in coming to study Physics at Nagoya University in the G30 Undergraduate Physics Program then you should contact the lecturer of this course before you make the decision to come to Japan.
WARNING ABOUT THE USE OF GENERATIVE AI
• Assignment exercises are an essential part of both the lecture course and the associated tutorial course. Students are thereby given the opportunity to master a wide variety of technical variations encountered in solving concrete examples of the basic theory, as well as a variety of simple extensions of the basic theory, and simple analytical techniques related to the lecture content but not mentioned in lectures, that extend the scope of problems that students can solve. Mastery of these aspects makes students more attractive to employers or future research labs.
• Reliance on generative AI is harmful to learning. In view of the importance of mastering the assignment exercises, measures will be put in place to ensure that students who rely on generative AI and group discussions to attain high assignment scores without mastering the content will not achieve an inflated final grade: inflated grades are unfair to students who take learning seriously and achieve scholarly independence by genuine hard work. After completing this course, if they do use AI to help with study, students should aim to be capable of critiquing the output from generative AI and evaluating its correctness -- in other words, they must be capable of solving the exercises as well as creative variations of the exercises and lecture content with no help. No employer wants employees who are unable to do this.
Face-to-face lectures, tutorials and exams are opportunities to demonstrate your scholarly independence. Even students who find mathematics difficult can attain at least a "B" grade by engaging in good study habits and learning the lecture content well, and by being honest with themselves and others.
All lecture course exams (Midsemester, End of Semester) are in-class. Students who rely on generative AI and do not master the content will reveal themselves when they are unable to make any meaningful progress with exam questions that are simple repetitions of assignment questions with minor changes or simple creative variations. Even students who have difficulty with mathematics can master such questions if they have good study habits and perseverence. Excessive reliance on generative AI and group discussions wastes time, harms your learning and affects your grades. |
| | 到達目標 【日本語】
Objectives of the Course(JPN)) | | | | 到達目標 【英語】
Objectives of the Course | | Objectives of the Course
The overriding objective of this course is to foster the student's scholarly independence. In order to succeed in this course, students must understand the content sufficiently to have the ability to potentially critique and evaluate the correctness of the output from group work, and generative AI if they use it, relevant to the lecture and assignment content. This is a transferable, real-world skill and, more importantly, mindset: the habit of checking before believing, while possessing the knowledge and technical ability to make the judgement.
Students will have the ability to solve problems such as creative variations of assignment exercises and lecture content with no help, and thereby demonstrate that they are capable of independently learning STEM knowledge and techniques, and are therefore potentially useful to future employers or university research groups. |
| | 授業の内容や構成
Course Content / Plan | | Some topics are covered in assignments. The precise order and content of the lectures might vary slightly.
Lecture 1. Revision of quantum statistical mechanics and preparation for this semester's material. Quantum states of a single particle. Reflecting boundary conditions, periodic boundary conditions. Density of states in 3, 2 and 1 dimensions, for linear and quadratic dispersion relations. Turning sums into integrals. Example: EM radiation. The quantum distribution functions: Fermi-Dirac, Bose-Einstein distributions. Photon statistics: Planck distribution. Systems with varying number of particles: the Grand Canonical ensemble and partition function. Occupation number formalism: mean occupation number and dispersion. Role of the chemical potential.
Lecture 2. Examples. Vapour pressure of a solid. Diatomic molecules. Grand Canonical partition function and probability of a many-body state at temperature T. Example: adsorption of a gas onto a 2D surface.
Lecture 3. The ideal Fermi fluid: conduction electrons in metals. Specific heat and ground state energy in 3D, 2D, 1D. Sommerfeld expansion.
Lecture 4. The ideal Bose fluid: Bose-Einstein condensation in 3D. What about in 2D or 1D? Critical temperature. Mean energy, specific heat.
Lecture 5. Relativistic Quantum Gas: the Photon Gas (Black body radiation). Planck's original argument. Bose's original paper two decades later justifying Planck's argument. Stefan-Boltzmann Law; Wien’s Displacement Law; radiation pressure; mechanical equation of state. NONEXAMINABLE: (if time allows) Classical theory of screening: the Debye-Hueckel Model.
Lecture 6. Introduction to Non-Ideal Systems (1): The Debye Model of solids. The Harmonic Approximation. Classical Theory. Quantized Theory. Normal modes. Phonons. The Debye Approximation. Specific heat. Rundown of main points in Ashcroft and Mermin Chapts 22,23 placing Debye Theory in perspective: Classical Theory of the Harmonic Crystal; Quantum Theory of the Harmonic Crystal.
Lecture 7. Introduction to Non-Ideal Systems (2). Weakly nonideal gases: virial expansion; 2nd virial coefficient and resulting equation of state. Derivation of the Van der Waals equation of state for a weakly non-ideal gas; derivation for a fluid using a self-consistent mean field approach. Derivation of 2nd virial coefficient and van der Waals Equation again, this time using Mayer f function. NONEXAMINABLE: The Cluster Expansion.
Lecture 8. Stability of thermodynamic systems. Concavity/convexity of thermodynamic potentials. Le Chatelier’s Principle. First Order phase transitions, features of the free energy. Discontinuity in the entropy: latent heat. Slope of the coexistence curves: Clausius-Clapeyron Equation. A Clausius-Clapeyron Equation for Magnetic Systems: Coexistence Curve of Superconducting and Normal Phases in a metal.
Lecture 9. Van der Waals fluid: unstable isotherms, physical isotherm, Maxwell equal-area rule. Multicomponent systems: Gibbs phase rule. Why does the phase diagram of water not have more than three phases coexisting at the same point?
Lecture 10. The Fluctuation-Dissipation Theorem. Response functions and correlations. Quantitative explanation of critical opalescence.
Lecture 11. Examples of phase transitions (order-disorder transition, which is a structural phase transition). Why do fluctuations get out of control near the critical point? Alben’s Model. Landau Theory: classical theory in the critical region. Order Parameter. Continuous phase transition. Spontaneous symmetry breaking. The critical exponents α,β,γ,δ and their classical values.
Lecture 12. Introduction to interacting magnetic systems: ferromagnetism and models for it. Ising model. 1D Ising chain with free ends. Mean field theory treatment of the 1D Ising chain. Effective field. Critical exponents.
Lecture 13. 1D Ising chain continued. No phase transition in the 1D Ising chain: proof by a simple argument; and by solving the model exactly. Exact solution of 1D Ising chain in zero field. Exact solution of 1D Ising ring with field switched on: transfer matrix. Spin correlation function: exact calculation for the 1D Ising chain. 2D Ising model on a square lattice (just mention): Exact critical exponents, behaviour of the specific heat. Phase diagram of ferromagnetic systems in 3D.
Lecture 14. Breakdown of the classical theory and advent of the modern theory. Cause of the breakdown (qualitative). Derivation of an inequality involving critical exponents – but all experiments suggest equality holds. Scaling hypothesis: ad hoc argument. Justification of the scaling hypothesis using Kadanoff’s block spins. Spatial renormalization group theory and sample calculation for the 1D Ising chain.
Lecture 15. Bogolyubov Variational Theorem. Order-Disorder Transition: constructing the Hamiltonian and deriving the optimal Mean Field Theory for its solution. Mean Field Theory for 1D Ising Model revisited. Transformation between Models and Universality classes: many problems that appear completely different are in fact manifestations of the same problem. Broken Symmetry, Universality Classes, and Goldstone’s Theorem (qualitative). NONEXAMINABLE: Modern (21st century) classification of phase transitions -- the new paradigm of topological phase.
Lecture 16. NONEXAMINABLE: 2D Ising model on a square lattice: Low-T solution -- Peierls Droplets; High-T solution; Kramers-Wannier Duality. Critical temperature for 2D Ising Model on a Square Lattice. Lee-Yang Zeroes and Phase Transitions. |
| | 履修条件
Course Prerequisites | | Prerequisites:
Statistical Physics II and Quantum Mechanics II; or Consent of Instructor.
Students must have passed Statistical Physics II to take Statistical Physics III.
Students must be very strong in physics and mathematics. |
| | 関連する科目
Related Courses | | Related Courses
Quantum Mechanics II; Physics Tutorial IVa; Statistical Physics II.
It is strongly advised that students concurrently enroll in Physics Tutorial IVa. |
| | 「履修取り下げ届」提出の要・不要
Necessity / Unnecessity to submit "Course Withdrawal Request Form" | | Necessity / Non-necessity to submit "Course Withdrawal Request Form"
A formal withdrawal form must be signed by the lecturer and submitted to the Student Office by the official withdrawal date in May. |
| | 履修取り下げの条件等
Conditions for Course Withdrawal | | Conditions for Course Withdrawal
A withdrawal request made after the May deadline will be rejected unless the circumstances are very exceptional.
If Statistical Physics III is NOT A COMPULSORY SUBJECT and the student plans never to take Statistical Physics III in the future, then a late withdrawal request will be considered.
However, I consider more favorably the case of students from departments other than Physics Science or Applied Physics Engineering who wish to take this course in order to learn the exciting ideas. |
| | 成績評価の方法と基準
Course Evaluation Method and Criteria | | Course Evaluation Method and Criteria
Attendance and class performance, attitude: 5%; Weekly quizzes or other written assessment: 30%; Midterm exam: 32.5%; Final Exam: 32.5%.
Some exam questions in the lecture course are simple repetitions of either tutorial or lecture assignment questions with minor changes or simple creative variations. If the student is unable to make meaningful progress with such exam questions during the exam, while in the assignment they presented quite a good solution, then the entire assignment corresponding to that question will be deemed to have a mark of 20%.
A certain subset of both Lecture Assignments and Tutorial Assignments must be submitted within a week of the midsemester exam. They will not be accepted after this, and will receive zero marks.
Be aware that mastering the assignments in both the tutorial course and lecture course is essential for performing well in the lecture course exams. You should view assignment work as preparation for the exams.
Students will only be permitted to sit the End of Semester Exam if they have submitted at least 4 out of 7 assignments by the date on which Lecture 15 is held.
Irrespective of how high the total assignment score is, in the two exams the student must demonstrate a sufficient understanding of all the basics: in particular, they must do well in the exam questions that are similar to certain assignment questions or that cover certain simple points in the lecture notes. Therefore, in principle, a student cannot pass the course if they score less than 45% on average in the two exams, even if they score 100% overall in assignments. |
| | 不可(F)と欠席(W)の基準
Criteria for "Fail (F)" & "Absent (W)" grades | | The “Absent” grade is reserved for students who withdraw by the official deadline in May. After that day, a letter grade will be awarded based on marks earned from all assessment during the semester.
If Statistical Physics III is NOT A COMPULSORY SUBJECT and the student plans never to take Statistical Physics III in the future, then a late withdrawal request will be considered. |
| | 参考書
Reference Book | | Reference Books/Recommended Reading
1. Hill, T., An Introduction to Statistical Thermodynamics, Dover, 1986. (Excellent introduction to Statistical Mechanics at Year 3 level. Alternative textbook. Highly recommended. Cheap to buy.)
2. Ashcroft & Mermin, Solid State Physics (Chapters 22,23 only).
3. Yeomans, J.M., Statistical Mechanics of Phase Transitions, Oxford Science Publications, 1992. (Simple, clear overview relevant to the second half of this course.)
4. Cardy, J., Scaling and renormalization in statistical physics, Cambridge Univ. Press, 1996. (Certain sections only.)
5. Shankar, R., Quantum Field Theory and Condensed Matter: An Introduction, Cambridge Univ. Press, 2017. (Certain sections only.)
6. Altland, A. & Simons, B., Condensed Matter Field Theory (2nd Ed.), Cambridge Univ. Press, 2010. (Mainly Chapter 1 only.)
7. Kittel, C. and Kroemer, H., Thermal Physics, W.H. Freeman. (Try as alternative to the above textbooks.)
8. Landau, L.D. and Lifshitz, E.M., Statistical Physics, Part I, by E.M. Lifshitz and L.P. Pitaevskii, Pergamon Press. (A classic book: thorough, advanced treatment. Highly recommended.)
9. Xiao-Gang Wen, Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford Graduate Texts), Oxford University Press Reissue edition (October 18, 2007).
For advanced students who want to experience the flavour of the current forefront in condensed matter physics and statistical mechanics. To understand this book thoroughly would be way beyond undergraduates – but that’s not the point: read the text and just scan the equations to get the flavour and excitement, the main ideas and how they link together to form the forefront of current thinking. Reach up from what you learn in SP3 and touch the sky. The condensed matter landscape has changed significantly in the 21st century largely due to new theoretical insights – especially the next paradigm after Landau (topological order), in whose introduction and widespread acceptance Wen himself has played a leading role – together with technological advances that create demand for understanding 2D materials. Crucial is the fact that unlike in particle physics, in condensed matter physics the turn-around time between a theoretical proposal and experimental acceptance or rejection can be as short as a few months, which creates the conditions for rapid development of the field, plenty of funding, and a healthy demand for graduate students. |
| | 教科書・テキスト
Textbook | | Textbook
1. Callen, Herbert, Thermodynamics and an Introduction to Thermostatistics, 2nd Ed., Wiley. (The Japanese translation has fewer misprints.)
2. Reif, F., Fundamentals of Statistical and Thermal Physics, McGraw-Hill, 1965.
3. Plischke, M. & Bergersen, B., Equilibrium Statistical Mechanics, 3rd Ed., World Scientific, 2006. |
| | 課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | Study Load (Self-directed Learning Outside Course Hours)
• This is a challenging course that requires a substantial time commitment.
• This course is part of your training to be a professional researcher. You are expected to revise the lecture notes, read and work through the textbook, and solve assignment problems outside lecture hours. You cannot learn physics by only attending lectures. The exams will consist of questions covering both lecture notes and assignments.
• Students must be willing to work hard if they wish to achieve a good, internationally competitive level. |
| | 注意事項
Notice for Students | | • Some exam questions in the lecture course are simple repetitions of either tutorial or lecture assignment questions with minor changes or simple creative variations. If the student is unable to make meaningful progress with such exam questions during the exam, while in the assignment they presented quite a good solution, then the entire assignment corresponding to that question will be deemed to have a mark of 20%.
• A certain subset of both Lecture Assignments and Tutorial Assignments must be submitted within a week of the midsemester exam. They will not be accepted after this, and will receive zero marks.
• Students will only be permitted to sit the End of Semester Exam if they have submitted at least 4 out of 7 assignments by the date on which Lecture 15 is held.
• Irrespective of how high the total assignment score is, in the two exams the student must demonstrate a sufficient understanding of all the basics: in particular, they must do well in the exam questions that are similar to certain assignment questions or that cover certain simple points in the lecture notes. Therefore, in principle, a student cannot pass the course if they score less than 45% on average in the two exams, even if they score 100% overall in assignments.
WARNING ABOUT THE USE OF AI
• Despite any rules and better ethical judgment, many of you will rely on AI (ChatGPT, Gemini, Sonnet, Claude etc.) to solve your assignment problems. Be aware that besides constituting academic misconduct and dishonesty, such use of AI is detrimental to your learning: among other things, you will lack the experience of getting stuck and digging your way out of a problem using your own knowledge, tenacity, ingenuity and creativity. You will not learn resilience in the field of study. The examinations are designed to test the quality of your learning, your ability to bring together multiple threads dealt with in lectures and assignments, your ability to interpret the equations and unify your understanding, to seek connections and dig your way out of a seeming dead end when solving a problem. You will not learn this by relying on AI. You will do very well in assignments but very poorly in the exams.
• Reliance on generative AI is harmful to learning. In view of the importance of mastering the assignment exercises, measures will be put in place to ensure that students who rely on generative AI and group discussions to attain high assignment scores without mastering the content will not achieve an inflated final grade: inflated grades are unfair to students who take learning seriously and achieve scholarly independence by genuine hard work. After completing this course, if they do use AI to help with study, students should aim to be capable of critiquing the output from generative AI and evaluating its correctness -- in other words, they must be capable of solving the exercises as well as creative variations of the exercises and lecture content with no help. No employer wants employees who are unable to do this.
Face-to-face lectures, tutorials and exams are opportunities to demonstrate your scholarly independence. Even students who find mathematics difficult can attain at least a "B" grade by engaging in good study habits and learning the lecture content well, and by being honest with themselves and others.
All lecture course exams (Midsemester, End of Semester) are in-class. Students who rely on generative AI and do not master the content will reveal themselves when they are unable to make any meaningful progress with exam questions that are simple repetitions of assignment questions with minor changes or simple creative variations. Even students who have difficulty with mathematics can master such questions if they have good study habits and perseverence. Excessive reliance on generative AI and group discussions wastes time, harms your learning and affects your grades. |
| | 他学科聴講の可否
Propriety of Other department student's attendance | | | Students from any department are welcome as long as they have the necessary grounding in mathematics and physics. |
| | 他学科聴講の条件
Conditions for Other department student's attendance | | | Students from any department are welcome as long as they have the necessary grounding in mathematics and physics. |
| | レベル
Level | | | | キーワード
Keyword | | | | 履修の際のアドバイス
Advice | | Advice
• Focus on your undergraduate studies. Resist distractions. Learn as much as you can. This period in your life is a golden opportunity that might never be repeated.
• It is strongly advised that students concurrently enroll in Physics Tutorial IVa.
• No solutions are handed out in class. It pays to come prepared and pay attention during the tutorial.
• Students must be willing to work hard if they wish to achieve a good, internationally competitive level.
• Assignment exercises are an essential part of both the lecture course and the associated tutorial course. Students are thereby given the opportunity to master a wide variety of technical variations encountered in solving concrete examples of the basic theory, as well as a variety of simple extensions of the basic theory, and simple analytical techniques related to the lecture content but not mentioned in lectures, that extend the scope of problems that students can solve. Mastery of these aspects makes students more attractive to employers or future research labs.
• Reliance on generative AI is harmful to learning. In view of the importance of mastering the assignment exercises, measures will be put in place to ensure that students who rely on generative AI and group discussions to attain high assignment scores without mastering the content will not achieve an inflated final grade: inflated grades are unfair to students who take learning seriously and achieve scholarly independence by genuine hard work. After completing this course, if they do use AI to help with study, students should aim to be capable of critiquing the output from generative AI and evaluating its correctness -- in other words, they must be capable of solving the exercises as well as creative variations of the exercises and lecture content with no help. No employer wants employees who are unable to do this.
Face-to-face lectures, tutorials and exams are opportunities to demonstrate your scholarly independence. Even students who find mathematics difficult can attain at least a "B" grade by engaging in good study habits and learning the lecture content well, and by being honest with themselves and others.
All lecture course exams (Midsemester, End of Semester) are in-class. Students who rely on generative AI and do not master the content will reveal themselves when they are unable to make any meaningful progress with exam questions that are simple repetitions of assignment questions with minor changes or simple creative variations. Even students who have difficulty with mathematics can master such questions if they have good study habits and perseverence. Excessive reliance on generative AI and group discussions wastes time, harms your learning and affects your grades. |
| | 授業開講形態等
Lecture format, etc. | | Face to face lectures and tutorials are compulsory (other than in exceptional circumstances; e.g. COVID infection). However, in order to record a video of the lecture -- including student interaction with each other and with the lecturer -- the lectures will simultaneously be carried out online using MS Teams. Students are therefore requested to bring their laptop or tablet to the lecture room. Make sure it has a microphone. Bring an electrical cord. For many G30 students, English is a 2nd or even 3rd language, so video recordings are an invaluable learning aid.
Live lectures via MS Teams (face-to-face and online). Before the start of semester students should ensure that they have correctly installed MS Teams using their THERS (国立大学法人東海国立大学機構 ) email account.
NUPACE students should contact Professor John Wojdylo before the start of semester for assistance with installing Teams correctly. |
| | 遠隔授業（オンデマンド型）で行う場合の追加措置
Additional measures for remote class (on-demand class) | | All lectures will be live face-to-face and online via MS Teams. Face-to-face attendance is compulsory (barring exceptional circumstances such as COVID infection).
A lecture video will be available immediately after each lecture to help with student revision.
The lecturer will be available to answer questions via Teams chat. |
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